Finite Math Examples

$1 \cdot ({(\frac{5}{6})}^{5} {(\frac{1}{6})}^{5 - 0})$

Step 1

Combine fractions.

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Step 1.1

Multiply ${(\frac{5}{6})}^{5} {(\frac{1}{6})}^{5 - 0}$ by $1$ .

${(\frac{5}{6})}^{5} {(\frac{1}{6})}^{5 - 0}$

Step 1.2

Simplify the expression.

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Step 1.2.1

Apply the product rule to $\frac{5}{6}$ .

$\frac{5^{5}}{6^{5}} {(\frac{1}{6})}^{5 - 0}$

Step 1.2.2

Raise $5$ to the power of $5$ .

$\frac{3125}{6^{5}} {(\frac{1}{6})}^{5 - 0}$

Step 1.2.3

Raise $6$ to the power of $5$ .

$\frac{3125}{7776} {(\frac{1}{6})}^{5 - 0}$

Step 1.2.4

Subtract $0$ from $5$ .

$\frac{3125}{7776} {(\frac{1}{6})}^{5}$

Step 1.2.5

Apply the product rule to $\frac{1}{6}$ .

$\frac{3125}{7776} \cdot \frac{1^{5}}{6^{5}}$

Step 1.3

Combine.

$\frac{3125 \cdot 1^{5}}{7776 \cdot 6^{5}}$

Step 1.4

One to any power is one.

$\frac{3125 \cdot 1}{7776 \cdot 6^{5}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $7776$ as $6^{5}$ .

$\frac{3125 \cdot 1}{6^{5} \cdot 6^{5}}$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3125 \cdot 1}{6^{5 + 5}}$

Step 2.3

Add $5$ and $5$ .

$\frac{3125 \cdot 1}{6^{10}}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $3125$ by $1$ .

$\frac{3125}{6^{10}}$

Step 3.2

Raise $6$ to the power of $10$ .

$\frac{3125}{60466176}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3125}{60466176}$

Decimal Form:

$5.16817865 \cdot 10^{- 5}$